Explanation, Existence and Natural Properties in Mathematics - A Case Study: Desargues’ Theorem

Lange, Marc

doi:10.1111/1746-8361.12120

Cited by 6 publications

(3 citation statements)

References 62 publications

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“…Many scientists and philosophers of science often implicitly hold that theories ought to be stated in high‐fidelity terminology 19 . Similarly, Lange (2015) has argued that genuinely explanatory mathematical proofs incorporate natural mathematical properties.…”

Section: Why Should (Some) People Care About Ideological Parsimony?mentioning

confidence: 99%

High‐Fidelity Metaphysics: Ideological Parsimony in Theory Choice

Finocchiaro

2021

Pacific Philosophical Qtr

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Many metaphysicians utilize the virtue‐driven methodology. According to this methodology, one theory is more worthy of endorsement than another insofar as it is more virtuous. In this paper, I show how a theory's overall virtue is shaped by its ideological parsimony – parsimony with respect to the terminology employed in stating the theory. I distinguish between a theory's truth and its fidelity (‘joint‐carvingness’) and the corresponding epistemic and fidelic virtues. I argue that ideological parsimony is not an epistemic virtue but is a fidelic virtue. Insofar as metaphysicians value fidelity, then, ideological parsimony has an important role in theory choice.

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Section: Why Should (Some) People Care About Ideological Parsimony?mentioning

confidence: 99%

High‐Fidelity Metaphysics: Ideological Parsimony in Theory Choice

Finocchiaro

2021

Pacific Philosophical Qtr

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“…Subsumption under a law isn't necessary, because many uncontroversially explanatory proofs just don't have this form. Consider for instance the proof of Desargues' theorem discussed in [Lange 2015], whose explanatoriness seems rather to lie in its 'exploit[ing] [a] feature of the given case that is similar to the remarkable feature of the theorem' (p. 438). (One could also consider the many explanatory proofs that succeed by transferring a problem to a geometric setting, or by making it otherwise visualizable.)…”

Section: An Argument From Philosophy Of Sciencementioning

confidence: 99%

Mathematical Explanation beyond Explanatory Proof

D’Alessandro¹

2020

The British Journal for the Philosophy of Science

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Much recent work on mathematical explanation has presupposed that the phenomenon involves explanatory proofs in an essential way. I argue that this view, ‘proof chauvinism’, is false. I then look in some detail at the explanation of the solvability of polynomial equations provided by Galois theory, which has often been thought to revolve around an explanatory proof. The article concludes with some general worries about the effects of chauvinism on the theory of mathematical explanation. 1Introduction2Why I Am Not a Proof Chauvinist 2.1Proof chauvinism and mathematical practice2.2Proof chauvinism and philosophy3An Example: Galois Theory and Explanatory Proof4Conclusion

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“…Another view that links mathematical explanation to metaphysics can be found in [Lange 2015] (see also chapter 9 of [Lange 2016]). Here Lange compares two types of proofs of Desargues' theorem on intersection points: one type which takes place in the setting of classical Euclidean geometry, and which takes the form of "a motley collection of special cases" ([Lange 2015], 438), and another type which achieves a unified treatment using methods from projective geometry.…”

Section: The Third Possibility: Identifying Dependence Relationsmentioning

confidence: 99%

Viewing-as explanations and ontic dependence

D’Alessandro

2018

Philos Stud

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According to a widespread view in metaphysics and philosophy of science (the "Dependence Thesis"), all explanations involve relations of ontic dependence between the items appearing in the explanandum and the items appearing in the explanans. I argue that a family of mathematical cases, which I call "viewing-as explanations", are incompatible with the Dependence Thesis. These cases, I claim, feature genuine explanations that aren't supported by ontic dependence relations. Hence the thesis isn't true in general. The first part of the paper defends this claim and discusses its significance. I argue, for example, that many mathematical explanations are apparently compatible with Dependence, so the existence of counterexamples is interesting and non-obvious. The second part of the paper considers whether viewing-as explanations occur in the empirical sciences, focusing on the case of so-called fictional models (such as Bohr's model of the atom). It's sometimes suggested that fictional models can be explanatory even though they fail to represent actual worldly dependence relations. Whether or not such models explain, I suggest, depends on whether we think scientific explanations necessarily give information relevant to intervention and control.This paper is about a certain mathematical phenomenon, and its implications for a widely held view about the metaphysics of explanation. I'll say more about the mathematical phenomenon shortly. The widely held view is this:Dependence Thesis: All explanations reflect relations of ontic dependence between the items appearing in the explanandum and the items appearing in the explanans.

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Explanation, Existence and Natural Properties in Mathematics - A Case Study: Desargues’ Theorem

Cited by 6 publications

References 62 publications

High‐Fidelity Metaphysics: Ideological Parsimony in Theory Choice

High‐Fidelity Metaphysics: Ideological Parsimony in Theory Choice

Mathematical Explanation beyond Explanatory Proof

Viewing-as explanations and ontic dependence

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